All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is not permissible for the woman’s guardian, i.e. the brother in this case, to make a condition on his sister's fiancé to tell his mother and family about the betrothal unless it is presumably known, almost with certainty, that if the husband's family do not know about the marriage, it would cause unbearable problems to the woman to be given in marriage, in which case, he has a right to make that condition. However, this condition should be outside the wedding contract, it neither makes lawful what is unlawful, nor makes unlawful what is lawful.
As this man is married and has children, it may be that his family would stand against his marriage to another woman, which might cause problems to the guardian's sister who is to be given in marriage. This condition may help save the woman from problems resulting from a second marriage, especially if the suitor lives with his parents in the same house.
Allaah Knows best.